




'''simple docstring'''







from __future__ import annotations

class 	_snake_case:






 def __init__(self       :  Any    ,		a       :  list[list[int]]    )       ->   Dict:






    """simple docstring"""


    A__       =     TypeError(
        'Matrices must be formed from a list of zero or more lists containing at '
        'least one and the same number of values, each of which must be of type '
        'int or float.'    )
    if len(a    ) != 0:
       A__       =     len(rows[0]    )
       if cols == 0:
          raise error
       for row in rows:
          if len(a    ) != cols:
             raise error
          for value in row:
             if not isinstance(a    ,		(int, float)    ):
                raise error
       A__       =     rows
    else:
       A__       =     []






 def 						_UpperCamelCase (self       :  Any    )       ->   list[list[int]]:






    """simple docstring"""


    return [[row[i] for row in self.rows] for i in range(len(self.rows[0]    )    )]






 @property
 def 						_UpperCamelCase (self       :  int    )       ->   int:






    """simple docstring"""


    return len(self.rows    )






 @property
 def 						_UpperCamelCase (self       :  int    )       ->   int:






    """simple docstring"""


    return len(self.rows[0]    )






 @property
 def 						_UpperCamelCase (self       :  str    )       ->   tuple[int, int]:






    """simple docstring"""


    return (self.num_rows, self.num_columns)






 @property
 def 						_UpperCamelCase (self       :  Optional[int]    )       ->   bool:






    """simple docstring"""


    return self.order[0] == self.order[1]






 def 						_UpperCamelCase (self       :  Tuple    )       ->   Matrix:






    """simple docstring"""


    A__       =     [
        [0 if column_num != row_num else 1 for column_num in range(self.num_rows    )]
        for row_num in range(self.num_rows    )
    ]
    return Matrix(a    )






 def 						_UpperCamelCase (self       :  int    )       ->   int:






    """simple docstring"""


    if not self.is_square:
       return 0
    if self.order == (0, 0):
       return 1
    if self.order == (1, 1):
       return int(self.rows[0][0]    )
    if self.order == (2, 2):
       return int(
           (self.rows[0][0] * self.rows[1][1])
           - (self.rows[0][1] * self.rows[1][0])    )
    else:
       return sum(
           self.rows[0][column] * self.cofactors().rows[0][column]
           for column in range(self.num_columns    )    )






 def 						_UpperCamelCase (self       :  List[Any]    )       ->   bool:






    """simple docstring"""


    return bool(self.determinant()    )






 def 						_UpperCamelCase (self       :  List[Any]    ,		a       :  int    ,		a       :  int    )       ->   int:






    """simple docstring"""


    A__       =     [
        [
            self.rows[other_row][other_column]
            for other_column in range(self.num_columns    )
            if other_column != column
        ]
        for other_row in range(self.num_rows    )
        if other_row != row
    ]
    return Matrix(a    ).determinant()






 def 						_UpperCamelCase (self       :  int    ,		a       :  int    ,		a       :  int    )       ->   int:






    """simple docstring"""


    if (row + column) % 2 == 0:
       return self.get_minor(a    ,		a    )
    return -1 * self.get_minor(a    ,		a    )






 def 						_UpperCamelCase (self       :  Any    )       ->   Matrix:






    """simple docstring"""


    return Matrix(
        [
            [self.get_minor(a    ,		a    ) for column in range(self.num_columns    )]
            for row in range(self.num_rows    )
        ]    )






 def 						_UpperCamelCase (self       :  Optional[int]    )       ->   Matrix:






    """simple docstring"""


    return Matrix(
        [
            [
                self.minors().rows[row][column]
                if (row + column) % 2 == 0
                else self.minors().rows[row][column] * -1
                for column in range(self.minors().num_columns    )
            ]
            for row in range(self.minors().num_rows    )
        ]    )






 def 						_UpperCamelCase (self       :  Dict    )       ->   Matrix:






    """simple docstring"""


    A__       =     [
        [self.cofactors().rows[column][row] for column in range(self.num_columns    )]
        for row in range(self.num_rows    )
    ]
    return Matrix(a    )






 def 						_UpperCamelCase (self       :  int    )       ->   Matrix:






    """simple docstring"""


    A__       =     self.determinant()
    if not determinant:
       raise TypeError('Only matrices with a non-zero determinant have an inverse'    )
    return self.adjugate() * (1 / determinant)






 def __repr__(self       :  Dict    )       ->   str:






    """simple docstring"""


    return str(self.rows    )






 def __str__(self       :  Dict    )       ->   str:






    """simple docstring"""


    if self.num_rows == 0:
       return "[]"
    if self.num_rows == 1:
       return "[[" + ". ".join(str(self.rows[0]    )    ) + "]]"
    return (
        "["
        + "\n ".join(
            [
                '[' + '. '.join([str(a    ) for value in row]    ) + '.]'
                for row in self.rows
            ]    )
        + "]"
    )






 def 						_UpperCamelCase (self       :  Any    ,		a       :  list[int]    ,		a       :  int | None = None    )       ->   None:






    """simple docstring"""


    A__       =     TypeError('Row must be a list containing all ints and/or floats'    )
    if not isinstance(a    ,		a    ):
       raise type_error
    for value in row:
       if not isinstance(a    ,		(int, float)    ):
          raise type_error
    if len(a    ) != self.num_columns:
       raise ValueError(
           'Row must be equal in length to the other rows in the matrix'    )
    if position is None:
       self.rows.append(a    )
    else:
       A__       =     self.rows[0:position] + [row] + self.rows[position:]






 def 						_UpperCamelCase (self       :  Optional[int]    ,		a       :  list[int]    ,		a       :  int | None = None    )       ->   None:






    """simple docstring"""


    A__       =     TypeError(
        'Column must be a list containing all ints and/or floats'    )
    if not isinstance(a    ,		a    ):
       raise type_error
    for value in column:
       if not isinstance(a    ,		(int, float)    ):
          raise type_error
    if len(a    ) != self.num_rows:
       raise ValueError(
           'Column must be equal in length to the other columns in the matrix'    )
    if position is None:
       A__       =     [self.rows[i] + [column[i]] for i in range(self.num_rows    )]
    else:
       A__       =     [
           self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
           for i in range(self.num_rows    )
       ]






 def __eq__(self       :  Optional[Any]    ,		a       :  object    )       ->   bool:






    """simple docstring"""


    if not isinstance(a    ,		a    ):
       return NotImplemented
    return self.rows == other.rows






 def __ne__(self       :  str    ,		a       :  object    )       ->   bool:






    """simple docstring"""


    return not self == other






 def __neg__(self       :  Tuple    )       ->   Matrix:






    """simple docstring"""


    return self * -1






 def __add__(self       :  int    ,		a       :  Matrix    )       ->   Matrix:






    """simple docstring"""


    if self.order != other.order:
       raise ValueError('Addition requires matrices of the same order'    )
    return Matrix(
        [
            [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns    )]
            for i in range(self.num_rows    )
        ]    )






 def __sub__(self       :  Union[str, Any]    ,		a       :  Matrix    )       ->   Matrix:






    """simple docstring"""


    if self.order != other.order:
       raise ValueError('Subtraction requires matrices of the same order'    )
    return Matrix(
        [
            [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns    )]
            for i in range(self.num_rows    )
        ]    )






 def __mul__(self       :  str    ,		a       :  Matrix | int | float    )       ->   Matrix:






    """simple docstring"""


    if isinstance(a    ,		(int, float)    ):
       return Matrix(
           [[int(element * other    ) for element in row] for row in self.rows]    )
    elif isinstance(a    ,		a    ):
       if self.num_columns != other.num_rows:
          raise ValueError(
              'The number of columns in the first matrix must '
              'be equal to the number of rows in the second'    )
       return Matrix(
           [
               [Matrix.dot_product(a    ,		a    ) for column in other.columns()]
               for row in self.rows
           ]    )
    else:
       raise TypeError(
           'A Matrix can only be multiplied by an int, float, or another matrix'    )






 def __pow__(self       :  Union[str, Any]    ,		a       :  int    )       ->   Matrix:






    """simple docstring"""


    if not isinstance(a    ,		a    ):
       raise TypeError('A Matrix can only be raised to the power of an int'    )
    if not self.is_square:
       raise ValueError('Only square matrices can be raised to a power'    )
    if other == 0:
       return self.identity()
    if other < 0:
       if self.is_invertable():
          return self.inverse() ** (-other)
       raise ValueError(
           'Only invertable matrices can be raised to a negative power'    )
    A__       =     self
    for _ in range(other - 1    ):
       result *= self
    return result






 @classmethod
 def 						_UpperCamelCase (cls       :  Tuple    ,		a       :  list[int]    ,		a       :  list[int]    )       ->   int:






    """simple docstring"""


    return sum(row[i] * column[i] for i in range(len(a    )    )    )


if __name__ == "__main__":
    import doctest

    doctest.testmod()








'''simple docstring'''







from typing import TYPE_CHECKING

from ...utils import (
    OptionalDependencyNotAvailable,
    _LazyModule,
    is_flax_available,
    is_tf_available,
    is_torch_available,
)


lowerCAmelCase_     						=				{
    '''configuration_roberta_prelayernorm''': [
        '''ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP''',
        '''RobertaPreLayerNormConfig''',
        '''RobertaPreLayerNormOnnxConfig''',
    ],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase_     						=				[
        '''ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''RobertaPreLayerNormForCausalLM''',
        '''RobertaPreLayerNormForMaskedLM''',
        '''RobertaPreLayerNormForMultipleChoice''',
        '''RobertaPreLayerNormForQuestionAnswering''',
        '''RobertaPreLayerNormForSequenceClassification''',
        '''RobertaPreLayerNormForTokenClassification''',
        '''RobertaPreLayerNormModel''',
        '''RobertaPreLayerNormPreTrainedModel''',
    ]

try:
    if not is_tf_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase_     						=				[
        '''TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''TFRobertaPreLayerNormForCausalLM''',
        '''TFRobertaPreLayerNormForMaskedLM''',
        '''TFRobertaPreLayerNormForMultipleChoice''',
        '''TFRobertaPreLayerNormForQuestionAnswering''',
        '''TFRobertaPreLayerNormForSequenceClassification''',
        '''TFRobertaPreLayerNormForTokenClassification''',
        '''TFRobertaPreLayerNormMainLayer''',
        '''TFRobertaPreLayerNormModel''',
        '''TFRobertaPreLayerNormPreTrainedModel''',
    ]

try:
    if not is_flax_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    lowerCAmelCase_     						=				[
        '''FlaxRobertaPreLayerNormForCausalLM''',
        '''FlaxRobertaPreLayerNormForMaskedLM''',
        '''FlaxRobertaPreLayerNormForMultipleChoice''',
        '''FlaxRobertaPreLayerNormForQuestionAnswering''',
        '''FlaxRobertaPreLayerNormForSequenceClassification''',
        '''FlaxRobertaPreLayerNormForTokenClassification''',
        '''FlaxRobertaPreLayerNormModel''',
        '''FlaxRobertaPreLayerNormPreTrainedModel''',
    ]


if TYPE_CHECKING:
    from .configuration_roberta_prelayernorm import (
        ROBERTA_PRELAYERNORM_PRETRAINED_CONFIG_ARCHIVE_MAP,
        RobertaPreLayerNormConfig,
        RobertaPreLayerNormOnnxConfig,
    )

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_roberta_prelayernorm import (
            ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
            RobertaPreLayerNormForCausalLM,
            RobertaPreLayerNormForMaskedLM,
            RobertaPreLayerNormForMultipleChoice,
            RobertaPreLayerNormForQuestionAnswering,
            RobertaPreLayerNormForSequenceClassification,
            RobertaPreLayerNormForTokenClassification,
            RobertaPreLayerNormModel,
            RobertaPreLayerNormPreTrainedModel,
        )

    try:
        if not is_tf_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_tf_roberta_prelayernorm import (
            TF_ROBERTA_PRELAYERNORM_PRETRAINED_MODEL_ARCHIVE_LIST,
            TFRobertaPreLayerNormForCausalLM,
            TFRobertaPreLayerNormForMaskedLM,
            TFRobertaPreLayerNormForMultipleChoice,
            TFRobertaPreLayerNormForQuestionAnswering,
            TFRobertaPreLayerNormForSequenceClassification,
            TFRobertaPreLayerNormForTokenClassification,
            TFRobertaPreLayerNormMainLayer,
            TFRobertaPreLayerNormModel,
            TFRobertaPreLayerNormPreTrainedModel,
        )

    try:
        if not is_flax_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_flax_roberta_prelayernorm import (
            FlaxRobertaPreLayerNormForCausalLM,
            FlaxRobertaPreLayerNormForMaskedLM,
            FlaxRobertaPreLayerNormForMultipleChoice,
            FlaxRobertaPreLayerNormForQuestionAnswering,
            FlaxRobertaPreLayerNormForSequenceClassification,
            FlaxRobertaPreLayerNormForTokenClassification,
            FlaxRobertaPreLayerNormModel,
            FlaxRobertaPreLayerNormPreTrainedModel,
        )

else:
    import sys

    lowerCAmelCase_     						=				_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)


